The French financial state prosecutor has requested that HSBC’s Swiss private bank be sent to criminal trial over a suspected tax-dodging scheme for wealthy customers.

The recommendation follows a lengthy investigation by local magistrates into alleged tax fraud involving 3,000 French taxpayers and is a procedural step that brings the Swiss banking arm one step closer to a possible trial in France.

The parent company HSBC, which faces a separate ongoing French investigation, said: “This is a normal step in the judicial procedure and the outcome of the matter is not determined as of today.”

Following the publication of files leaked by IT expert turned whistleblower Hervé Falciani, the global bank has admitted wrongdoing at Swiss arm but insists things have changed

The bank has one month to respond after which French magistrates will take the final decision on whether to hold a trial.

Le Monde reported that HSBC refused a plea deal that would have avoided a trial. It said HSBC would have had to pay a €1.4bn fine as part of that deal.

HSBC has admitted failings in compliance and controls in its Swiss bank and faces investigation by US authorities and an inquiry by British MPs after reports that it helped customers conceal millions of dollars of assets in a period up to 2007.

Cases against specific clients of the Swiss bank are already in progress in France.

HSBC faces 10 separate inquiries around the world into the scandal. The US Department of Justice is considering criminal charges against the bank and its clients and the bank is under investigation in Brazil, India, Belgium and other jurisdictions.

HSBC’s chief executive, Stuart Gulliver, has admitted that the revelations are a source of shame and the chairman, Douglas Flint, has said they are “deeply humbling”. The two have pledged to clean up the bank but say they cannot be held responsible for the Swiss bank’s actions.

The Guardian reported that Gulliver had an account at the Swiss private bank and that he also used a Panamanian company to channel his earnings. He admitted the arrangement, which he ended in 2009, looked strange but said it was to protect his privacy and was not related to tax.

Margaret Hodge, chair of the UK’s public accounts committee, has called on Rona Fairhead, who is a non-executive HSBC director, to resign as chair of the BBC Trust over the scandal.

Pressure also increased on Flint this week when Robert Jenkins, a former Bank of England policymaker, called on him to quit as HSBC chairman to preserve his own reputation and that of the bank.

The Swiss revelations came on top of a $1.9bn (£1.3bn) fine imposed on HSBC in the US for flouting sanctions and allowing its Mexican arm to launder money for drug gangs.

Arlette Ricci, the millionaire heiress to the Nina Ricci fashion and perfume house, went on trial last month in Paris accused of hiding more than $22m from French tax authorities via a bank account at HSBC’s Swiss arm.

The trial, held in a special new Paris court to deal with tax fraud, was seen as a test case – Ricci was among the first clients to go on trial over money held via HSBC’s Swiss private bank. More than 60 wealthy French people have been formally investigated since a list of thousands of clients alleged to have evaded taxes through HSBC’s Swiss private bank became public.

Ricci, 73, a French psychoanalyst and writer, was on trial alongside her daughter and accountant. All denied charges of tax fraud and money-laundering.

The French state prosecutor recommended Ricci be sentenced to two years in prison, plus two years’ suspended sentence and a €3m fine. The judges will return their verdict on 13 April.